We report on the observation of controllable spatial separation in a
dual-species Bose-Einstein condensate (BEC) with $^{85}$Rb and $^{87}$Rb.
Interparticle interactions between the different components can change the
miscibility of the two quantum fluids. In our experiments, we clearly observe
the immiscible nature of the two simultaneously Bose-condensed species via
their spatial separation. Furthermore the $^{85}$Rb Feshbach resonance near 155
G is used to change them between miscible and immiscible by tuning the
$^{85}$Rb scattering length. Our apparatus is also able to create $^{85}$Rb
condensates with up to $8\times10^4$ atoms which represents a significant
improvement over previous work

Papp, S. B.

Pino, J. M.

Wieman, C. E.

English

arXiv

We report on the observation of controllable phase separation in a dual-species Bose-Einstein condensate with 85Rb and 87Rb. Interatomic interactions between the different components determine the miscibility of the two quantum fluids. In our experiments, we can clearly observe immiscible behavior via a dramatic spatial separation of the two species. Furthermore, a magnetic-field Feshbach resonance is used to change them between miscible and immiscible by tuning the 85Rb scattering length. The spatial density pattern of the immiscible quantum fluids exhibits complex alternating-domain structures that are uncharacteristic of its stationary ground state.</p

Wieman, Carl E.

CU Scholar Institutional Repository

arXiv:0802.2591v1  [cond-mat.other]  19 Feb 2008Studying a dual-species BEC with tunable interactionsS. B. Papp,1, ∗ J. M. Pino,1 and C. E. Wieman2, 11JILA, National Institute of Standards and Technology and University of Colorado, Boulder, Colorado 80309-0440, USA2University of British Columbia, Vancouver, BC V6T 1Z1, CANADA(Dated: February 12, 2013)We report on the observation of controllable spatial separation in a dual-species Bose-Einsteincondensate (BEC) with 85Rb and 87Rb. Interparticle interactions between the different componentscan change the miscibility of the two quantum fluids. In our experiments, we clearly observe theimmiscible nature of the two simultaneously Bose-condensed species via their spatial separation.Furthermore the 85Rb Feshbach resonance near 155 G is used to change them between miscibleand immiscible by tuning the 85Rb scattering length. Our apparatus is also able to create 85Rbcondensates with up to 8 × 104 atoms which represents a significant improvement over previouswork.Two-component quantum fluids have long been knownto exhibit rich physics that is not accessible in a sim-ple single-component fluid [1]. The miscibility of twoquantum fluids represents a fundamental property of atwo-component system, and it is partially controlled byinterparticle interactions. Building on the achievementof dilute-gas Bose-Einstein condensation [2], mixtures ofultracold quantum gases provide a unique system forthe study of interacting multi-component quantum flu-ids. Moreover resonant control of two-body interactionsin ultracold gases is possible via magnetic-field Feshbachresonances [3] and provides a parameter which directlyalters the miscibility of the dual-species BEC.The first two-component condensate was producedwith different hyperfine states of 87Rb, and evidence forrepulsive interactions between the hyperfine states wasreported [4]. Further work with different hyperfine statesof 87Rb studied the dynamics of interpenetrating quan-tum fluids [5]. In spinor condensates of Na both misci-ble and immiscible two-component condensates were ob-served for the first time [6]. In further work, long-livedmetastable excited states were realized with spinor Nacondensates [7, 8]. More recently a dual-species BEC of41K and 87Rb was reported in Ref. [9] where scissors-likecollective oscillations were observed as a result of off-axiscollisions.Two-component quantum gases have also long beenthe subject of significant theoretical interest; topics ofstudy include the density pattern and phase separationof the components [10, 11, 12, 13, 14, 15] and the spec-trum of collective excitations [16, 17]. Spatial separationof two immiscible quantum fluids in a trap is typifiedby a ball-and-shell ground-state structure in which onefluid forms a low density shell around the other. Thisstructure depends on the relative strength of interspeciesand single-species interactions [10]. Other ground-statestructures are expected as well and a general classifica-tion of all possible ground-state spatial structures hasbeen presented in Ref. [18]. A mixture of 85Rb and87Rb has long been considered a promising experimentalsystem for studying two interpenetrating quantum flu-ids, and a route to dual-species BEC with Rb was pro-posed in Ref. [19]. The tendency for spatial separationto occur in a 85Rb –87Rb mixture can be predicted byapplying the theoretical analysis of Refs. [20, 21] for theThomas-Fermi limit. Based on their analysis we definethe parameter∆ =a85 a87a285−87− 1 (1)that depends upon the ratio of the single species and in-terspecies interactions. In the case where a85−87 is posi-tive two regimes emerge: ∆ > 0 where the two conden-sates are miscible and ∆ < 0 where they are immiscibledue to the strong interspecies repulsion. For simplicitywe have neglected the small difference in mass of 85Rband 87Rb here.In this Letter we report the production of a dual-species BEC of 85Rb and 87Rb with tunable interactions.Immiscibility of the two-component quantum gas is ob-served as a dramatic departure in the density distributionfrom that of the symmetry of the external trapping po-tential. Surprisingly we observe the robust formation ofmultiple, non-overlapped, single-species BEC “cloudlets”which represent an interesting metastable excited state.We find that the degree of spatial separation betweenthe two species can be controlled with a tunable 85Rbscattering length.Our apparatus and evaporative cooling routine are de-scribed in Ref. [24]. Atoms are initially collected froma vapor into a two-species magneto-optical trap (MOT).After magnetic transfer to another region of the appa-ratus with lower vacuum pressure the atoms are pre-pared into the 85Rb |f = 2, mf = −2〉 state and87Rb|f = 1, mf = −1〉 state and loaded into a magnetic trap.Selective rf evaporation is used to lower the temperatureof the 87Rb gas to 10 µK, while the 85Rb gas is sympa-thetically cooled through thermal contact with the 87Rb[25]. The two-species gas is then loaded into an opticaldipole trap [Fig. 1], while maintaining a large, nearlyuniform magnetic field. Further evaporation to BEC isperformed by lowering the depth of the optical potential.2(a)(b) (c)Ibias85 87opticaltrapyyzzgravityIbiasFIG. 1: (a) Schematic drawing of the optical trap laser beamand the magnetic-field coils. The curvature of the magneticfield enhances confinement along the axial direction (z) of theoptical trap. The center position of the trapping potentialalong its axis is influenced by the tilt of the optical trap rel-ative to gravity, and the relative position of the optical trapbeam focus and the coils. Optical trap tilt and misalignmentof the beam focus and the coils have been exaggerated forclarity. Absorption images are acquired along the axis whichis into the page. (b, c) Absorption images of single-species85Rb and 87Rb condensates which demonstrate the smoothsingle-species density profiles consistent with the shape of thetrapping potential. Prior to absorption imaging, the gas isreleased from the optical trap and it expands for 20 ms; themagnetic field remains on for the first 10 ms of expansion toprevent collapse of the 85Rb gas [22, 23].Unless otherwise noted, after evaporation the depth ofthe optical trap is raised in 50 ms to ∼ 1µK with a mea-sured 85Rb radial (axial) trap frequency of 2π × 130 Hz(2π × 2.9 Hz). While the 87Rb radial frequency is nearlyidentical to that of 85Rb, the axial frequency (2π × 2.6Hz) is smaller due to a different magnetic moment andthe curvature of the magnetic field.To create a 85Rb BEC it is important to use a weaklyconfining optical trap to reduce density-dependent inelas-tic loss and to control the scattering length of 85Rb us-ing the Feshbach resonance. Specifically, condensates arecreated only in a small range of magnetic field near 163.1G where the 85Rb interaction is repulsive [26, 27] and in-elastic collision rates are sufficiently small. By optimiz-ing the evaporation rate and the precise number ratio ofthe two species at the start of evaporation, we are ableto create a single-species 85Rb BEC with up to 8 × 104atoms, a 87Rb BEC with 2×106 atoms, or a BEC of bothspecies. Absorption images of single-species condensatesafter expansion are shown in Fig. 1. The elongated ax-ial direction (z) of all the absorption images in this papershow the spatial density of the gas since the trapping fre-quency is small. The images show the momentum densityin the radial direction (y). Several interspecies Feshbachresonances are accessible in our system including the s-wave resonances used in Ref. [24] as well as recentlydiscovered p-wave resonances at 257.8 G and ≈ 330 G[28]. For the magnetic fields used in this work, however,the interspecies scattering length is +213(7) a0 [29] andthe 87Rb scattering length is +99 a0 [30].-200 -100 0 100 20001234-200 -100 0 100 20001234summedOD(104)position (mm)summedOD(104)position (mm)(a)(a)(e)(f)(c)(b)(d)(b)(d)(c)87878585a a85 = 51 0a a85 = 51 0a a85 = 780 0a a85 = 780 0D = -0.89D = 0.72yzFIG. 2: Absorption images at two different 85Rb scatteringlengths that display immiscible (a,b) and miscible (c,d) be-havior. Each image in the pairs (a,b) and (c,d) were acquiredwith different condensates after creation under the same con-ditions. The sum of each image pair should be interpreted asthe total density of the expanded gas. (e, f) The measuredtwo-dimensional optical density (OD) was summed in the re-maining radial direction to produce a cross section. The 85Rbscattering length was 51 a0 for images (a, b) and it was 780a0 for images (c, d). The number of85Rb (87Rb) atoms isapproximately 4× 104 (9× 104).Interesting physics occurs when we create a simulta-neously Bose-condensed sample of 85Rb and 87Rb. Thedual BEC exhibits either miscible or immiscible behav-ior, depending on the magnetic field, as seen in Fig. 2.3After preparation of a dual species BEC, the magneticfield was swept in 400 ms from 163.1 G to a value in therange of 164.6 G to 158.6 G; the sweep covered a range in∆ of approximately -1 to +1 (50 a0 to 900 a0). The rateof this sweep was measured to be slow with respect to theresponse of the gases in the radial and axial directions ofthe trap. Absorption images of each gas were acquiredafter the sweep. The images are shown for ∆ = −0.89[Fig. 2 (a) and (b)] and ∆ = 0.72 [Fig. 2 (c) and (d)].We observe a dramatic spatial separation of the two gaseswhen ∆ is negative. The irregular spikes in the densitypatterns of the two condensates will be discussed in moredetail below. When ∆ is positive, the coexistence of eachspecies throughout the axial direction is observed andthe sharp density spikes of the immiscible condensatesgive way to a smooth overall density. Spatial separationwas observed to return when the magnetic-field sweepto ∆ > 0 was immediately followed by a second oppositefield sweep to ∆ < 0. The penetration distance in the ax-ial direction over which the two expanded gases overlap isestimated to be approximately 30 µm when ∆ = −0.89.To characterize the degree of spatial separation as ∆ isvaried, we have extracted the axial center-of-mass loca-tion of each species from images similar to those shownin Fig. 2. In this experiment an offset between the axialtrap centers for each species was intentionally introduced[Fig. 1 (a)] to reflect the spatial separation in the center-of-mass location. The offset causes the two immisciblequantum gases to separate primarily in the axial direc-tion with each species preferring a well-defined side ofthe trap. The results of this experiment are plotted inFig. 3 as a function of ∆. The centers of each BEC grad-ually come together as ∆ is increased from -0.9 towardzero. For ∆ > 0 there is little change as the two speciescan then coexist throughout the trap. However, residualgravitational sag likely induces incomplete spatial over-lap even when ∆ > 0 [20].We have studied the different immiscible density pat-terns as a function of the number of each Rb species.We vary the relative number in the two-species MOTto change the number of atoms in the BECs. Figure 4shows absorption images of both 85Rb and 87Rb conden-sates immediately after evaporation to a fixed final trapdepth of ≈100 nK, and ∆ = −0.82 (81 a0) so that thetwo quantum fluids are always immiscible. In each imagea different condensate is shown since the measurementprocess is destructive. The trap was not recompressedin order to accentuate the spatial separation of the twospecies.When a condensate of each species is present in thetrap we observe “holes” in the 87Rb image that corre-spond to “spikes” at approximately the same location inthe 85Rb image [Fig. 4 (a)-(d)]. This behavior is con-sistent with spatial separation of two immiscible quan-tum fluids. However the images are not consistent withany known phase-separation structure expected for the-1.0 -0.5 0.0 0.5 1.0-50-250255085Rb  axial gas position (µm)∆87RbFIG. 3: Measured axial position of the 85Rb and 87Rb gasesas a function of the parameter ∆. We report the uncertaintyin the position as the shot-to-shot reproducibility of our mea-surements. When ∆ > 0 the measured difference in the posi-tion of each gas is in good agreement with that expected forsingle-species condensates.ground state of a two-component system as described inRef. [18]. The 85Rb gas is observed to split into multipleseparated cloudlets that appear as distinct holes in the87Rb gas. In Fig. 4 (a) and (b) two 85Rb cloudlets areobserved, and three cloudlets are observed in image (c).These images represent long-lived presumably metastableexcited states of the two-component system that dependon the relative number of each species. If the initial num-ber of 85Rb atoms at the start of evaporation is too large,the 87Rb gas cannot be cooled to condensation and re-mains a dilute thermal gas; in this case [Fig. 4 (e)] the85Rb condensate shape is unperturbed and well approx-imated by a Thomas-Fermi model.The immiscible gases shown in Fig. 4 are not symmet-ric with respect to either the radial or axial directionsof the trap. These asymmetries are caused by gravita-tional sag of the trap and can be reduced by recompres-sion to increase the trap depth [Fig. 4 (f)]. Symmetryin the radial direction is restored but spatial separationis still clearly observed along the axial dimension. Sim-ilarly we have verified that offsets in the center-of-massaxial position of each species can be controlled via pre-cise alignment of the optical trap focus with respect tothe magnetic field [Fig. 1 (a)]. Although the preciseshape, size, and position of the immiscible gases is af-fected by details of the trapping potential, the observa-tion of spatial separation and the formation of separated85Rb cloudlets is repeatable under a variety of experi-mental conditions. The spatial separation and cloudletbehavior are observed during the evaporation process as485Rb87Rb(a)(b)(c)(d)(e)(f)yzFIG. 4: (a-e) Absorption images of 85Rb (left column) and87Rb (right column) condensates demonstrating the immisci-bility of the quantum gases. For clarity the OD of each 87Rbimage was scaled by a factor of 0.5 and the size of each imageis 330 µm × 150 µm. The number of 85Rb particles variesfrom approximately 1.2 × 104 in (a) to 2.2 × 104 in (e); the87Rb number varies from 1.4 × 105 in (a) to 3 × 103 in (e).For comparison absorption images of single species 85Rb and87Rb condensates are shown in Fig. 1 (b, c). (f) Absorp-tion images following recompression of the optical trap thatdemonstrate a symmetrical radial distribution.soon as the temperature of both species is lowered belowthe condensation temperature. Furthermore, the dual-species BEC remains spatially separated and individualcloudlets of 85Rb do not coalesce during the 1 sec lifetimeof the 85Rb BEC, which includes many radial and a fewaxial trap oscillations.We lack a detailed theoretical understanding of 85Rbcloudlet formation in our experiments. The geometry ofour system is complicated by the elongated axial direc-tion of the trap with an aspect ratio near 50 and thepresence of gravitational sag. In an analysis of the fa-vorability for cloudlet formation the energy cost of form-ing and maintaining extra boundary surface area mustbe weighed against the cost of all particles residing inthe same cloud [13]. These questions appear to requirethe solution of coupled Gross-Pitaevskii equations for thedual-species BEC wave-functions which is beyond thescope of this paper [12]. Recent theoretical simulationsof our system have obtained qualitative agreement withthe data presented here [31].In summary, we have produced a dual-species BEC of85Rb and 87Rb with tunable interactions. Immiscibilityof the two quantum fluids was observed as a departurein the gas density pattern from that expected due to thesymmetry of the potential. By varying the 85Rb scat-tering length the degree of spatial separation was char-acterized. Surprisingly immiscible condensates are ob-served to form multiple spatially-separated cloudlets. 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Studying a Dual-Species BEC with Tunable Interactions

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Studying a dual-species BEC with tunable interactions

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